Possibility of fully spin-polarized nodal chain state in several spinel half metals

Nodal-chain fermions, which are novel topological states of matter, have been hotly discussed in the field of nonmagnetic materials. Here, by using first-principles calculations and symmetry analysis, we propose the realization of a fully spin-polarized nodal chain in several spinel half metals, including ${\mathrm{LiV}}_{2}{\mathrm{O}}_{4}, {\mathrm{VMg}}_{2}{\mathrm{O}}_{4}, {\mathrm{FeAl}}_{2}{\mathrm{O}}_{4}$, and ${\mathrm{NiAl}}_{2}{\mathrm{O}}_{4}$. In these materials, the ferromagnetic state takes on a half-metal band structure, and only the bands from the single channel are present near the Fermi level. Taking ${\mathrm{LiV}}_{2}{\mathrm{O}}_{4}$ as an example, we show how the crossing of bands in the spin-up channel forms two types of nodal loops. These nodal loops arise from band inversion and are under the protection of the glide mirror symmetries. Remarkably, we find that the nodal loops join with each other and form a chainlike nodal structure. Correspondingly, the $\ensuremath{\omega}$-shaped surface states are also fully spin-polarized. The fully spin-polarized nodal chain identified here has not been proposed in realistic materials before. An effective model is constructed to describe the nature of the nodal chain. The effects of the electron correlation, the lattice strains, and the spin-orbit coupling are discussed. The fully spin-polarized bulk nodal chain and the associated nontrivial surface states for a half metal may pave the way for additional applications in spintronics.